33.1.2.2 Marotzke's scheme

1.

Same as step (1) above, except that the stability of all pairs of grid cells is checked, odd and even pairs (so that the density of interior levels is computed twice, for two different reference pressures).

2.

Don't mix yet: just mark all unstable pairs and find continuous regions of the water column which are unstable (neutral stability is treated as unstable).

3.

Mix the unstable regions.

4.

If there was instability in any column, repeat steps (1) to (3). Those columns which were completely stable in the previous round are not dealt with again in (2) and (3), but the densities are still recomputed for the entire grid row. Repeat until no more instabilities are found.

So Marotzke relaxed the condition that only two levels are mixed at a time, and complete mixing will be achieved with at most k-1 passes through the water column, if k is the number of model levels. However, if only one grid point of a row requires n iterations, the densities for the entire grid row will be recomputed n times, so it still doesn't look too good in terms of cpu efficiency.